Two significant consequences of quantum fluctuations are entanglement and criticality. Entangled states may not be critical but a critical state shows signatures of universality in entanglement. A surprising result found here is that the entanglement entropy may become arbitrarily large and negative near the dissociation of a bound pair of quantum particles. Although apparently counterintuitive, it is shown to be consistent and essential for the phase transition, by mapping to a classical problem of DNA melting. We associate the entanglement entropy to a sub-extensive part of the entropy of DNA bubbles, which is responsible for melting. The absence of any extensivity requirement in time makes this negative entropy an inevitable consequence of quantum mechanics in continuum. Our results encompass quantum critical points and first-order transitions in general dimensions.
Two significant consequences of quantum fluctuations are entanglement and criticality. Entangled states may not be critical but a critical state shows signatures of universality in entanglement. A surprising result found here is that the entanglement entropy may become arbitrarily large and negative near the dissociation of a bound pair of quantum particles. Although apparently counterintuitive, it is shown to be consistent and essential for the phase transition, by mapping to a classical problem of DNA melting. We associate the entanglement entropy to a sub-extensive part of the entropy of DNA bubbles, which is responsible for melting. The absence of any extensivity requirement in time makes this negative entropy an inevitable consequence of quantum mechanics in continuum. Our results encompass quantum critical points and first-order transitions in general dimensions.
The conformational properties of a DNA molecule when mapped onto a Heisenberg spin system denaturation transition can be formulated in terms of quantum phase transition induced by a quench where the temperature effect is incorporated in the quench time. Here torsion takes on the role of the external field. The denaturation transition occurs when the entanglement entropy of the spin system vanishes. As the critical region corresponds to a two-limit behaviour the entanglement entropy gradually decreases with the gradual increase in the fraction of open base pairs and when the entropy vanishes the two strands are separated. The sequence heterogeneity interplays with the entropy effects and we have the onset of denaturation bubbles. We have studied the melting profiles for different sequence-specific DNA molecules and the results are found to be in excellent agreement with experiment.
When a DNA molecules conformational characteristics are charted adjacent to a Heisenberg-spin-system, the denaturation shift be able to be expressed in stipulations of a QFT (quantum-phase-transition) brought on through a quench, in which the external field is torsion and the temperature effect is integrated into the quench time. When the spin system's entanglement entropy disappears, the denaturation transition takes place. The energy of torsion includes temperature, stress, and torque, the latter of which is correlated with the twist angle. A DNA molecule put on the Heisenberg spin chain experiences torsion as the outer field. When the EE (entanglement entropy) disappears, the transition to denaturation takes place. The entanglement entropy steadily drops as the proportion of unlock stand pairs gradually increases, the two strands split until the entropy disappears, since the dangerous area corresponding to a 2-boundary actions. The melting profiles of specific DNA molecules have been examined, and the findings show great agreement with biotechnology.
Abstract Entanglement plays a key role in quantum physics, but how much information it can extract from many-body systems is still an open question, particularly regarding quantum criticalities and emergent symmetries. In this work, we systematically study the entanglement entropy (EE) and derivative entanglement entropy (DEE) near quantum phase transitions in various quantum many-body systems. A one-parameter scaling relation between the DEE and system size at the critical point has been derived for the first time, which successfully obtains the critical exponent via data collapse. Furthermore, we find that the EE peaks at the (emergent) symmetry-enhanced first-order transition, reflecting higher symmetry breaking. This work provides a new paradigm for quantum many-body research from the perspective of EE and DEE.
We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S A = −Tr ρ A logρ A corresponding to the reduced density matrix ρ A of a subsystem A . For the case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c , we re-derive the result of Holzhey et al when A is a finite interval of length in an infinite system, and extend it to many other cases: finite systems, finite temperatures, and when A consists of an arbitrary number of disjoint intervals. For such a system away from its critical point, when the correlation length ξ is large but finite, we show that , where is the number of boundary points of A . These results are verified for a free massive field theory, which is also used to confirm a scaling ansatz for the case of finite size off-critical systems, and for integrable lattice models, such as the Ising and XXZ models, which are solvable by corner transfer matrix methods. Finally the free field results are extended to higher dimensions, and used to motivate a scaling form for the singular part of the entanglement entropy near a quantum phase transition.
Entanglement is a fundamental feature of quantum mechanics and plays an important role in characterizing many-body systems and quantum phase transitions. A quantitative measure of quantum correlations between subsystems is entanglement entropy. In this thesis, we study the entanglement entropy of an interacting quantum field theory, the O(N) model. In local quantum field theories, the leading-order contribution in the scaling of entanglement entropy obeys an area law. This dominant term is governed by short-distance physics near the entangling surface and depends on the ultraviolet regularization, making it non-universal. Beyond this lead- ing scaling behavior, entanglement entropy can contain subleading universal contributions, which encode intrinsic information about the underlying quantum field theory. In this thesis, we calculate one such universal term: the correlation length coefficient r, which appears as a correction to the entanglement entropy evaluated slightly away from the quantum critical point. The analysis is carried out in D = 2 + 1 spacetime dimensions for an infinite cylindrical geometry. We study the model in the vicinity of criticality using the large-N expansion, which enables controlled analytical calculations. Our main result is that the coefficient r scales linearly with the number of field components N . This behavior is consistent with the interpretation of r as a universal quantity associated with the degrees of freedom of the theory. The calculation is based on the replica method and renormalization group arguments, which are presented in detail. Finally, we discuss the physical meaning of the result and possible methods for verifying it, and we review related results for the O(N) model in different geometries.
We study the bipartite von Neumann entropy of two particles interacting via a long-range scale-free potential V ( r ) ∼ − g / r 2 in three dimensions, close to the unbinding transition. The nature of the quantum phase transition changes from critical (−3/4 < g < 1/4) to first order ( g < −3/4) with g = −3/4 as a multicritical point. Here, we show that the entanglement entropy has different behaviours for the critical and the first-order regimes. But there still exists an interesting multicritical scaling behaviour for all g ∈ ( − 2 < g < 1/4) controlled by the g = −3/4 case.